\version "2.18.2"

% "square" transpositions linked to the defined row

#(define (squareNumber n) (squareTranspose row n))

% List the rows that will be written

#(define (squareRows n) (pset-op 12transpose row (squareTranspose row n)))

% Convert the numbers in the row to Lilypond pitches

#(define (number->note n)
   (cond
    ((= n 0) (ly:make-pitch 1 0))
    ((= n 1) (ly:make-pitch 1 0 1/2))
    ((= n 2) (ly:make-pitch 1 1))
    ((= n 3) (ly:make-pitch 1 1 1/2))
    ((= n 4) (ly:make-pitch 0 2))
    ((= n 5) (ly:make-pitch 0 3))
    ((= n 6) (ly:make-pitch 0 3 1/2))
    ((= n 7) (ly:make-pitch 0 4))
    ((= n 8) (ly:make-pitch 0 4 1/2))
    ((= n 9) (ly:make-pitch 0 5))
    ((= n 10) (ly:make-pitch 0 5 1/2))
    ((= n 11) (ly:make-pitch 0 6))
    (else (error "Pitch not found"))))

% Write elements (markups or note)

writeElements = #(define-music-function (parser location sym1 sym2 fn1 ls) (symbol? symbol? procedure? list?)
   (make-music 'SequentialMusic 'elements
     (let loop ((ls ls))
       (if (null? ls)
           '()
           (cons 
            (make-music
             sym1 ;'LyricEvent / 'NoteEvent
             sym2 ; 'text / 'pitch
             (fn1 (car ls)) ; (markup #:concat (#:larger "RI" #:sub (number->string (car ls)))) / (number->note (car ls))
             'duration
             (ly:make-duration 2))
            (loop (cdr ls)))))))

% customBarLine by Janek Warchoł
% http://stackoverflow.com/questions/18538793/lilypond-markup-text-next-to-barline
% changed to write the Retrograde inversion

customBarLine = #(define-music-function (parser location n) (number?)
                   #{
                     \once \override Staff.BarLine #'stencil =
                     #(lambda (grob)
                        (ly:stencil-combine-at-edge
                         (ly:bar-line::print grob)
                         X RIGHT
                         (grob-interpret-markup grob 
                           #{ \markup {
                             \whiteout
                               \vcenter
                               \concat {
                                 \larger "R" \sub #(number->string (squareNumber n))}
                           } #}) 
                         0))#})

% Write a new Staff with the transposition number:
%% - As an instrument name on the left
%% - As a custom bar line on the right

writeRow =  #(define-music-function (parser location n) (number?)
               #{ 
                 \new Staff \with { 
                   instrumentName = \markup { \concat { \larger O \sub #(number->string (squareNumber n)) } } 
                 }
                 {
                   \writeElements #'NoteEvent 
                   #'pitch
                   #(lambda (x) (number->note x))
                   #(squareRows n)
                   \stopStaff
                   \bar "|"
                   s4
                   \customBarLine #n 
                 }
               #})

% Write markups with a large string and a subtexted number

writeRowMarkups = #(define-music-function (parser location str ls) (string? list?)
              #{
                \writeElements #'LyricEvent
                                  #'text
                                  #(lambda (x) 
                                     (markup #:concat (#:larger str #:sub (number->string x))))
                                  #ls
              #})

% Use writeRowMarkups to write the inversion transpositions

markupI = #(define-music-function (parser location) ()
                 #{
                   \writeRowMarkups #"I" #(zero-pset row 12)
                 #})

% Use writeRowMarkups to write the retrograde-inversion transpositions

markupRI = #(define-music-function (parser location) ()
                 #{
                   \writeRowMarkups #"RI" #(zero-pset row 12)
                 #})

% Recursive function to write the 12 rows with all the transpositions

writeRowRec = #(define-music-function (parser location n) (number?)
                 (if (= 12 n)
                     #{ #}	
                     #{ 
                       <<
                         \writeRow #n  
                         \writeRowRec #(+ n 1)
                       >>
                     #}))

writeSquare = \writeRowRec #0